On the page where it talks about commas (http://www.grammar-monster.com/punctuation/using_commas.htm), it explicitly states that "bread, milk, and cheese", with a comma after 'milk', is an americanism, and that "bread, milk and cheese", without a comma after 'milk' is the British way of putting it.
http://www.oxforddictionaries.com/words/what-is-the-oxford-comma will explain that, in actual fact, putting the comma after milk is the correct British way of doing it, and it is colloquial hooliganism which has lead to the omission of that, in highly rare and unintellectual cases that are few and far between; I should know, I'm currently being schooled in the UK!
As I'm sure that, on this site, you strive towards the education of proper grammar, I thought I'd point this minor discrepancy out.
You can't cite the Oxford dictionary to support a case for the Oxford comma. That's a circular argument. (It's a bit like asking your mum whether you're good looking.)
I'm happy with the page as it is. The Oxford comma is more common in America than it is in the UK. In the UK, many consider it a waste of ink. That said, I find myself using it more often these days because so many Americans read this site, and they expect it. For an English-only audience, I wouldn't use an Oxford comma unless it eliminated ambiguity.
Just use the rules as set by your exam board. The one thing to watch out for is comma splices; it is better to avoid them, even permitted exceptions in looser English. Teachers hunt them. A new sentence should be preceded either, depending on context by: m-dash, for extra information ;or comma with conjunction, for compound, or semicolon, for closely related sentence ;or full stop, for new sentence. It's best to avoid comma splice exceptions like 'sentence bla bla, I didn't.' -- 'I didn't' although small is still a sentence to the hounding teacher and requires ',and' or ';' or '--' or '.' depending on context.
